There’s some truth in this. Depends on a couple of things, though, imo.
Firstly, what are Paratici’s views? If he feels the same as Conte - should he leave - then he perhaps goes too. He was supposedly instrumental in getting Conte to come and they obviously have a close relationship. Will he want to stick around for another manager? We have a history of ploughing through people in these types of positions too (e.g. Paul Mitchell, who said). For both to go would seem a huge backward step.
Secondly, Pochettino, Mourinho and Conte all walking away dissatisfied (and trophy-less) from the club within just over three years is not a good look generally - or to other prospective managers. We seemed to struggle to fill the position last time (hence the Nuno debacle), let’s remember.
My biggest worry should Conte go is that Levy’s desperation to appease the fans will see him reappoint Pochettino. Much as I love the bloke I don’t think him coming back will be a receipe for success unfortunately - certainly not so soon after him leaving previously.
My hope is that Conte stays and the board give him what he needs: a couple of the established wing-backs that he wants, alongside at least one CB and a creative midfielder.